# Jaywalking your dog: Computing the Fréchet distance with shortcuts

A. Driemel, S. Har-Peled

12 Citaten (Scopus)

## Samenvatting

The similarity of two polygonal curves can be measured using the Fréchet distance. We introduce the notion of a more robust Fréchet distance, where one is allowed to shortcut between vertices of one of the curves. This is a natural approach for handling noise, in particular batched outliers. We compute a constant factor approximation to the minimum Fréchet distance over all possible such shortcuts. Our algorithm runs in O(c^2 kn log^3 n) time if one is allowed to take at most k shortcuts and the input curves are c-packed. For the case where the number of shortcuts is unrestricted, we describe an algorithm which runs in O(c^2 n log^3 n) time. To facilitate the new algorithm we develop several new data-structures, which we believe to be of independent interest: (i) for range reporting on a curve, and (ii) for preprocessing a curve to answer queries for the Fréchet distance between a subcurve and a line segment.
Originele taal-2 Engels Proceedings of the 23rd Annual ACM-SIAM Symposium on Discrete Algorithms (SODA'12),17-19 january 2012, Kyoto, Japan Y. Rabani Society for Industrial and Applied Mathematics (SIAM) 318-327 978-1-61197-210-8 https://doi.org/10.1137/1.9781611973099.30 Gepubliceerd - 2012 Ja 23rd Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2012) - Westin Miyako, Kyoto, JapanDuur: 17 jan 2012 → 19 jan 2012Congresnummer: 23http://www.siam.org/meetings/da12/

### Congres

Congres 23rd Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2012) SODA '12 Japan Kyoto 17/01/12 → 19/01/12 23rd Annual ACM-SIAM Symposium on Discrete Algorithms http://www.siam.org/meetings/da12/